# Negative predictive value

Last revised by Stefan Tigges on 4 Sep 2024

Negative predictive value (NPV) is one of the 4 basic diagnostic test metrics in addition to sensitivity, specificity and positive predictive value. Negative predictive value is a measure of how often someone who tests negative for disease does not have disease and is calculated by dividing the number of true negatives (TN) by the number of people who tested negative, i.e. true negatives and false negatives (FN):

• TN/(TN + FN)

The formula shows that a high NPV is achieved by maximizing true negatives and minimizing false negatives.

Negative predictive value can be expressed as a conditional probability:

• P(Disease negative |Test negative)

Bayes' theorem can be used to calculate NPV if sensitivity, specificity, and pretest probability (p) are known:

• NPV = [(specificity) x (1 - p)] / [specificity x (1 - p) + (1 - sensitivity) x (p)]

Unlike sensitivity and specificity, NPV depends to some extent on disease prevalence. When prevalence increases, NPV decreases because the proportion of true negatives to false negatives decreases. For example, if the entire population of interest had disease, all of the negatives would be false negatives, there would be no true negatives, resulting in a NPV of 0%. When prevalence decreases, NPV increases because the proportion of true negatives to false negatives increases. For example, if no one in the population of interest had disease, all of the negatives would be true negatives, there would be no false negatives, resulting in a NPV of 100%. Positive predictive value and negative predictive value move in opposite directions as prevalence increases or decreases.